Is space-time interaction real or apparent in seismic activity?

It is widely shared opinion that not only secondary (aftershocks) but also main earthquakes have the tendency to occur in space-time clusters. This assumption has affected the preferential choice of stochastic models in the studies on seismic hazard, like self-exciting (epidemic) models which imply the abrupt increase of the occurrence probability after a shock and the subsequent exponential decrease without the desirable increase before a forthcoming event. The importance of this assumption requires the application of statistical tools to evaluate objectively its coherence with the reality at different scale of magnitude-space-time. To this end we consider the earthquakes drawn from the historical Italian catalogue CPTI04 that geologists have associated with each of the eight tectonically homogeneous regions in which Italian territory is divided. Fixing different magnitude thresholds we perform statistical tests based on the space-time distance between pairs of earthquakes under the null hypothesis of uniform distribution in time and space and evaluate the significance of the possible clusters. Monte Carlo hypothesis testing is also used to obtain the null distribution and the simulated p-value.